Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks

Area of Science:

• Complex Systems Research
• Nonlinear Dynamics
• Time Series Analysis

Background:

• Characterizing nonlinear, stochastic, and high-dimensional systems presents significant challenges in complex systems research.
• Distinguishing between chaotic and stochastic signals, and quantifying temporal correlations, remain open questions.
• Existing methods struggle with the complexity of empirical signals from such systems.

Purpose of the Study:

• To develop a reliable technique for differentiating chaotic from stochastic signals.
• To quantify nonlinear and high-order temporal correlations in time series data.
• To provide a robust method applicable to complex systems research.

Main Methods:

• A novel approach combining artificial neural networks (ANNs) and symbolic ordinal analysis.
• Training an ANN with flicker noise to predict the correlation parameter [Formula: see text].
• Utilizing permutation entropy (PE) differences to distinguish between stochastic and chaotic signals.

Main Results:

• The ANN-derived [Formula: see text] parameter effectively indicates temporal correlations in time series.
• A significant difference in PE between a time series and flicker noise signifies chaotic behavior.
• The technique demonstrates robustness across varying time series lengths and noise levels.

Conclusions:

• The proposed technique reliably differentiates chaotic from stochastic signals.
• It accurately quantifies temporal correlations using ANNs and symbolic ordinal analysis.
• This freely available algorithm offers a valuable tool for complex systems research.